Abstract
Let (W, S) be a Coxeter group associated to a Coxeter graph which has no multiple bonds. Let H be the corresponding Hecke Algebra. We define a certain quotient \-H of H and show that it has a basis parametrized by a certain subset W cof the Coxeter group W. Specifically, W cconsists of those elements of W all of whose reduced expressions avoid substrings of the form sts where s and t are noncommuting generators in S. We determine which Coxeter groups have finite W cand compute the cardinality of W cwhen W is a Weyl group. Finally, we give a combinatorial application (which is related to the number of reduced expressions for w ∈ W cof an exponential formula of Lusztig which utilizes a specialization of a subalgebra of \-H.
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Fan, C.K. A Hecke Algebra quotient and some combinatorial applications. J Algebr Comb 5, 175–189 (1996). https://doi.org/10.1007/BF00243786
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DOI: https://doi.org/10.1007/BF00243786